Nonlinear transport through a dynamic impurity in a strongly interacting one-dimensional electron gas

We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to the voltage sources. Assuming the impurity time dependence to be oscillatory, we present a full analytic perturbative result in impurity strength for arbitrary interaction parameter calculated with the help of Coulomb gas expansion (CGE). Moreover, a full analytic solution beyond the above restriction is possible for a special nontrivial interaction strength which has been achieved independently by full resummation of CGE series as well as via refermionization technique. The resulting nonlinear current-voltage characteristic turns out to be very rich due to the presence of the additional energy scale associated with the impurity oscillation frequency. In accordance with the previous studies, we also find an enhancement of the linear conductance of the wire to values above the unitary limit $G_0=2e^2∕h$.

Figure 1

Perturbative differential conductance as function of impurity oscillation for various values of $g⩽1∕2$ for ${\lambda }^{\prime }=0.8$ and ${\Delta }^{\prime }=\pi$. $G_d$ exceeds $G_0$ at a critical frequency ${\Omega }_0$. In the inset: Dependence of the critical impurity frequency ${\Omega }_0$ on the interaction strength $g$.

Figure 2

Perturbative linear conductance for $g=0.2$ as function of applied voltage $U$ for different values of $\Omega ∕{\lambda }_B$, where ${\lambda }_B=\pi {\lambda }^2∕\Delta$. For small applied voltages, the conductance exceeds $G_0$ for $g<1∕2$.

Figure 3

Conductance as a function of bias voltage for different impurity oscillation frequencies at zero temperature. In the inset: Weakening of the ZBA with increasing oscillation frequency.